Literally, to be able to undergo cold turkey narcotics withdrawal without the usual helpless uncontrollable diarrhea. Figuratively, to be tough, to undergo hardships without losing it.

"She was in that jail cell for three days going cold after her last shot of H, and never a peep. That broad can really hold her mud."
"She's going through an evil divorce and never once badmouthed her ex. She can really hold her mud."